If an electron revolves in the path of radius of $0.5\times {10}^{-10}m$ at a frequency of $5\times {10}^{15}$ cycles $S^{-1}$, then find the electric current in the circle.

CONCEPT:

Electric current:

• The flow of electric charges through a conductor constitutes an electric current.
• Quantitatively, electric current in a conductor across an area held perpendicular to the direction of flow of charge is defined as the amount of charge flowing across that area per unit time i.e.,

$\mathrm{E}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{r}\mathrm{i}\mathrm{c}\mathrm{c}\mathrm{u}\mathrm{r}\mathrm{e}\mathrm{r}\mathrm{n}\mathrm{t}\left(\mathrm{I}\right)=\frac{\mathrm{E}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{r}\mathrm{i}\mathrm{c}\mathrm{c}\mathrm{h}\mathrm{a}\mathrm{r}\mathrm{g}\mathrm{e}\left(\mathrm{Q}\right)}{\mathrm{T}\mathrm{i}\mathrm{m}\mathrm{e}\left(\mathrm{t}\right)}$

• SI unit of current is ampere and it is denoted by the letter A.

CALCULATION:

Given - Radius of circle (r) = 0.5 × 10^-10 m and frequency (f) = 5 × 10¹⁵ s^-1

• The electric current can be written mathematically as,

$\Rightarrow I=\frac{Q}{t}$

Q = 1.6 × 10-19 C

• As we know, reciprocal of time period gives frequency i.e.,

$\Rightarrow I=\frac{Q}{t}=Q\times f$                   $[\because f=\frac{1}{t}]$

⇒ I = 1.6 × 10^-19 ×5 × 1015 = 8 × 10^-4 A = 0.8 mA